Arbitrary Orientations Of Hamilton Cycles In Oriented Graphs

Luke Kelly

Published 2009-07-20, updated 2009-08-06Version 2

We use a randomised embedding method to prove that for all \alpha>0 any sufficiently large oriented graph G with minimum in-degree and out-degree \delta^+(G),\delta^-(G)\geq (3/8+\alpha)|G| contains every possible orientation of a Hamilton cycle. This confirms a conjecture of H\"aggkvist and Thomason.